198
ISSN 1392ndash1207 MECHANIKA 2016 Volume 22(3) 198205
Fault diagnosis for supporting rollers of the rotary kiln using the
dynamic model and empirical mode decomposition
Kai Zheng Yun Zhang Chen Zhao Tianliang Li School of Mechanical and Electronic Engineering Wuhan University of Technology Wuhan 430070 China
E-mail zhengkai2001163com
School of Mechanical and Electronic Engineering Wuhan University of Technology Wuhan 430070 China
E-mail whkascoaliyuncom
School of Mechanical and Electronic Engineering Wuhan University of Technology Wuhan 430070 China
E-mail zhaochenwhuteducn
School of Mechanical and Electronic Engineering Wuhan University of Technology Wuhan 430070 China
E-mail tianliangliwhutsinacom
httpdxdoiorg105755j01mech22313072
1 Introduction
Rotary kiln is a typical large slow-speed running
(2-6 rpm) mechanical equipment As key equipment rotary
kiln is widely used in the cement industry metallurgical
industry and environmental protection industry It is main-
ly composed by transmission system driving system sup-
porting rollers and heat exchange system [1] as shown in
Fig 1 The plain bearings in the supporting rollers enable
the rotary kiln to run at a low speed with heavy load (12
supporting rollers support 15000-20000 kN load) [1-2]
And the operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
[1-3] During long-term operation supporting rollers vi-
brate due to the kiln crank [2] Early fault diagnosis for the
rotary kilnrsquos supporting rollers has important engineering
significance in that it can help to reduce equipment
maintenance cost and economic loss resulting from pro-
duction suspension of the rotary kiln [1-2] To achieve the
above-mentioned purposes it is of great importance to
study the dynamic model and identify the fault features of
the supporting rollers
Until now a limited research has been done for
the fault diagnosis of the supporting rollers Eng Zbignie
et al have studies the causes of the kiln crank and pointed
that the kiln crank would affect the supporting bearings
and lead to the deflection of the supporting rollersrsquo shaft
[4] Świtalski Maciej proposed a method for the diagnostic
of the rotary kilnrsquos technical state by the measurement of
the shellrsquos elastic [6] Alma Žiga Hertz et al studied the
distribution of contact pressure between the supporting
roller and tyre based on Hertz contact theory and did a
simulation research based on finite element method [7]
Gebhart Walter et al proposed the measurement principle
and method of the supporting rollerrsquos deflection They
adopted curve fitting method to calculate the deflection of
the roller shaft [3] Xj Li et al presented that dynamic
change of the operating axis of the rotary kiln will lead to
complex vibration of the equipment so as to speed up fa-
tigue failure of the supporting rollers They used transfer
matrix method to establish a kinetic model of the rotary
kilnrsquos cylinder [8] Stamboliska Zhaklina Eugeniusz
Rusiński et al studied the cause of the vibration of the
rotary kilnrsquos supporting rollers and pointed out that the
vibration of the supporting rollers essentially resulted from
the kiln crank of rotary kilns cylinder Meanwhile they
made an in-depth study on the fault mode of the supporting
rollers and proposed an online signal processing method
based on the FFT method [1-2]
However few work has been involved the vibra-
tion mechanism and the fault extraction of the supporting
rollers In order to explore the impact of the crank of the
rotary kilnrsquos cylinder on the supporting rollers as well
make fault diagnosis this paper put forward the dynamic
model of the supporting rollers and made a numerical sim-
ulation analysis Moreover as the vibration signals of the
supporting rollers are normally characterized with nonsta-
tionary behaviour to analyze the vibration signals with
nonstationary properties we presented features extraction
and fault diagnosis method of the rotary kiln supporting
rollers based on empirical mode decomposition (EMD) so
as to realize the condition monitoring of the low-speed
operation rotary kiln
The remainder of this paper is organized as fol-
lows In Section 2 an analysis was made on the impact of
the rotary kiln crank on the supporting rollers and the dy-
namic model was established In Section 3 the numerical
simulation analysis was done In Section 4 a features ex-
traction and fault diagnosis method based on empirical
mode decomposition was presented In Section 5 an
analysis was made on the vibration signals from the indus-
try field experiment based on the numerical simulation
analysis result and the proposed the fault diagnosis method
Section 6 is a conclusion of this paper
Fig 1 Rotary kiln in a cement plant of China
199
2 Physical model of the supporting rollers
21 The effect to supporting rollers of kiln operation
According to FMECA result the fault of the sup-
porting rollers is a main factor which can lead to the
breakdown of the rotary kiln [1-2] According to [3] the
fault of the supporting rollers is mainly caused by the kiln
crank generated by the internal thermal process of the ro-
tary kiln During long-term operation the profile of the
cylinder will change which will lead to misalignment be-
tween the geometric center and the rotation center thereby
causing the eccentricity of the cylinder section And the
dynamic load caused by the deformation of the cylinder
eccentricity gives rise to the vibration of the supporting
roller The snowball effect in the rotary kilnrsquos cylinder will
further intensify the vibration of the supporting rollers
According to [1] the materials will form a basic ball in the
kiln called the snowball effect during the operation of the
rotary kiln The ball moves slowly around the kilnrsquos axis
When the weight of the snowball exceeds the adhesive
force on the kiln coating and the snowball surface the
snowball will come off from the kiln coating Under ex-
treme conditions such a thermal effect may lead to signif-
icant load unbalance of the supporting rollers
Fig 2 shows the straightness deviation of the ro-
tary kiln we measured in a cement plant in China It can be
found that the straightness deviation of rotary kiln cylinder
was large due to various factors The supporting rollers in
the three stations of the rotary kiln are free from the re-
straint of the tyre When the snowball effect appears in the
rotary kilnrsquos cylinder the straightness deviation of the axis
will increase leading to heavy cyclic loads which will
cause the vibration of supporting rollers in the radial direc-
tion as shown in Fig 3 If the vibration amplitude is too
large the plain bearing may not make up the displacement
of the roller shaft so as to cause frictional heating in them
And the bearing alloy will melt with the high temperature
causing significant failure of the supporting rollers
Fig 2 The measurement result of straightness deviation of
the rotary kiln in a cement plant
Fig 3 The vibration of supporting rollers caused by the
Kiln crank effect
To establish the dynamic equation of the support-
ing rollers it is very important to describe the cyclic load
resulting from the kiln crankAccording to [2 4] the
change of the kiln cylinder profile is an important factor
resulting in the dynamic load and the eccentricity (e) can
be used as a main parameter for assessing the section pro-
file To establish the dynamic model of the supporting roll-
ers a simplified formula was put forward for the cyclic
load calculation And it can be expressed as
2
1 1 1f m e (1)
Where m1 is the equivalent unbalance mass at the
corresponding station ω1 is the kiln cylinderrsquos rotational
speed and e1 is the eccentricity of the cylinderrsquos cross sec-
tion
22 The equations of the supporting rollers
To establish the dynamic model of the low-speed
rotary kilnrsquos supporting system under cyclic load we es-
tablished a simplified model as shown in Fig 4 In Fig 4
supposing that the rotary kilnrsquos supporting roller is a disc
with a mass m the supporting shaft is an isotropic shaft
without mass and the left and right rollers at the same po-
sition of the rotary kiln bear the same load and that OXY is
the inertial coordinate system Oxy is the rotating coordi-
nate system O is the whirling center (rotation center) of
the supporting roller Orsquo is the centroid R is the radius of
the supporting roller e is the eccentricity of the center sec-
tion of the supporting roller We can derive the equation of
the supporting rollerrsquos vibration according to Lagranges
dynamical equations
a b
Fig 4 The model schematic of supporting rollers a - side
view b - front view
According to the force analysis for the supporting
rollers the external loads of them can be expressed by
Eqs (2)
2
1
2
1
n
j
n
j
F f cos tme cos t
f sin tme cos tQ
(2)
where f is the cyclic load caused by the kiln crank ω is the
rotation speed of the supporting roller and e is the eccen-
tricity of the supporting roller Based on Lagranges dy-
namical equations and formulas (2) we can derive the dy-
namic equation of the supporting roller as expressed by
Eq (3)
200
1 1
2 2
0 00
0 00
n
j
n
j
Fc km x x x
c km y Qy y
(3)
where k1 and k2 are the stiffness values of the supporting
roller in x and y directions c1 and c2 are the damping forc-
es of the supporting roller in x and y directions respec-
tively as we suppose the supporting roller is isotropous it
can be regarded that k1 = k2 c1 = c2 m is the equivalent
mass of the supporting roller
3 Numerical prediction for the response of supporting
rollers
31 The simulation parameters estimation
It is great important to carry out a careful estima-
tion of the physical parameter values of the supporting
rollers to perform a numerical simulation However it is
difficult to take this task as that the specific parameters of
the support rollers depend on the production the length
and the tyre number of a rotary kiln In this research we
take a qualitative analysis to the numerical simulation of a
three tryes rotary kiln with the production of
5000-6500 dt According to [9] the basic material of the
supporting rollers is ZG42GrMo and the elasticity modulus
of it is 209 times 105 MPa The mass density of the rollers is
786 times 10-6 kg mm3 and the radius is 1150 mm Based on
the above data we can obtain the approximate physical
parameter values of supporting rollers which are shown in
Table 1
Table 1
Estimation parameters of the supporting rollers
used for numerical simulations
Parameter Value
Rollers stiffness of x y axis k1 k2 148 times 105 N m
Rollers viscous damping of x y
axis c1 c2 692 times 104 Ns m
Equivalent mass of rollers m 405 times 104 kg
Equivalent imbalance mass of
station2 m1 797 times 105 kg
The rotating speed of the rollers ω 107 r min
The rotating speed of the kiln ω1 4 r min
Mass unbalance angle β 0 rad
32 Numerical analysis of the supporting rollers
In this section the dynamic response of the sup-
porting rollers under the influence of the kiln cylinder
crank was studies The influence of the cyclic load to sup-
porting rollers caused by thermal effects of the kiln cylin-
der was stimulated
As it is difficult to achieve analytical solution of
the complex dynamics equation the numerical methods
was used to solve the problem And the fourth-order
Runge-Kutta method [10] is selected to solve the Eq (10)
to obtain the dynamics response of the supporting rollers
The effect on the supporting rollers of the rotary
kiln crank was analyzed in this section According to sec-
tion II during the operation of the kiln it will change the
dimensional size as the result of the internal thermal pro-
cesses As the rotation center and the center of mass is not
overlap in the cylinder section thus producing section ec-
centricity Therefore the eccentricity of the cross section
can be used as a main parameter to represent the kiln crank
And we compared the vibration response of the supporting
roller under whether or not there is kiln crank And the
simulation result was shown in Fig 5 Furthermore the
relationship between the section eccentricity of the kiln
cylinder and the amplitude of the kiln harmonic and the
amplitude of the rollers harmonic was analyzed and the
result was shown in Fig 6
a
b
Fig 5 The vibration response in the y direction of the sup-
porting rollers when e1 = 3 and e1 = 10 mm a - time
domain b - frequency domain
Fig 6 Relationship between the section eccentricity of the
kiln cylinder and the amplitude of the kiln harmonic
and the amplitude of the rollers harmonic
From the above numerical simulation results it
can be found that
1) when there is kiln crank there will have a kiln
harmonics (KH) in the vibration signal
2) when the magnitude of the kiln harmonic
201
(KH) increased it is a sign that the crank of the rotary kiln
is being enhanced And it has larger deviations from the
normal operation in terms of eccentricity and deflections
from regular rotation axis in section corresponding to mon-
itored station
3) the frequency of kiln harmonic is consistent
with rotary kiln rotating speed while the frequency of roll-
ers harmonic is equal to the supporting rollers rotation
speed Therefore the operation condition of the rotary kiln
can be monitored by collecting the vibration signals of the
supporting rollers
4 Feature extraction using empirical mode
decomposition method
As mentioned in section 3 the vibration signals of
the supporting rollers contain multiple fault information
According to the numerical analysis for the supporting
rollers it can be found that the vibration signal mainly
includes the harmonic component caused by the kiln crank
and the harmonic component caused by the deflection of
the roller shaft In [17] authors pointed out that it also
contains the harmonic component of the surface character-
istic such as the harmonic component of waviness the
roughness and micro-irregularities In fact the vibration
signal are nonlinear non-stationary signal which are not
suitable processed by the traditional signal processing
method such as fast Fourier transform (FFT) or Wavelet
transform (WT) [12-14] In this research we proposed a
method for feature extraction of supporting rollers based
on empirical mode decomposition
41 Empirical mode decomposition
Empirical mode decomposition was first proposed
as a part of HilbertndashHuang transform (HHT) by Norden
Ehuang which is effective method to analysis the nonlin-
ear non-stationary signal [13] As the key part of HHT the
method of EMD to decompose signal is intuitive direct
and adaptive This decomposition method is based on local
characteristic of local time domain of signals Based on
this characteristic any linear stationary or nonlinear
non-stationary signal can be decomposed into a set of In-
trinsic Mode Functions (IMFs) which are amplitude and
frequency modulated signals It has been proven to be an
effective method in analyzing nonstationary signals for
rotational machine fault detection [15 16] According to
[15 16] each IMF satisfies two basic conditions
1) over the entire dataset the number of extreme
and the number of zero crossings must either be equal or
differ at most by one
2) at any time point the local mean value of the
envelope which defined by the average of the maximum
and minimum envelopes is zero
The specific processes of EMD are described as
follows
Step 1 For the given signal x(t) construct its up-
per envelope emax(t) and lower envelope emin(t) by connect-
ing all local maxima and local minima with cubic spline
functions And
11
2
max mine t e t
m
(4)
Step 2 Compute the envelopes mean m11 and
x(t) ndash m11 = h1(t) And the definition of IMF is proposed
mainly to get the physical meaning of the instantaneous
frequency
Step 3 If h1(t) satisfies the definition of IMF then
we can obtain the first-order IMF IMF1 = h1(t) And then
go to the next step In addition the IMF component
c1(t) = h1k(t) is saved If it is not the IMF repeat Steps 1ndash3
The stop condition for the iteration is given by
2
1
20
1
iji jT
t
i j
h t h tSD
h t
(5)
where hi(j-1)(t) and hij(t) denote the IMF candidates of the
j ndash 1 and j iterations respectively and usually SD is set
between 02 and 03
Step 4 Separate c1(t) from x(t) we could get
r1(t) = x(t) ndash c1(t) r1(t) is treated as the original data and
repeat the above processes the second IMF component c2(t)
of x(t) could be got Let us repeat the process as described
above for n times then n-IMFs of signal x(t) could be got
Step 5 The decomposition process can be stopped
when r(n)(t) becomes a monotonic function from which no
more IMF can be extracted We can finally obtain
1
n
i nix t c t r
(6)
Residue r(n)(t) is the mean trend of x(t) The IMFs
c1(t) c2(t) cn(t) include different frequency bands
ranging from high to low The frequency components con-
tained in each frequency band are different and they
change with the variation of signal x(t) while r(n)(t) repre-
sents the central tendency of signal x(t)
42 Feature extraction and fault diagnosis procedure
Numerical simulation results shown that the kiln
harmonic (KH) and the rollers harmonic (RH) will lead to
significant change as the kiln cylinder crank happens or the
rollers behavior changes Therefore the energy variation of
the kiln harmonic (KH) and the rollers harmonic (RH) of
the vibration signals can reflect the running condition of
the rotary kiln When the malfunction occur in a mechani-
cal equipment the energy of the vibration signal would
change strongly in some frequency bands but in other fre-
quency bands the energy maybe change weakly [12] Ac-
cording to [16] the IMF energy moment not only contains
the size of IMFs energy but also considers the distribution
of IMFrsquos energy change with the time parameter t It can
be used to express the energy distribution of the fault
characteristic frequency component for the vibration sig-
nals In this research the IMFrsquos energy moment is em-
ployed for fault diagnosis of the supporting rollers And the
procedures are summarized as follows
Step 1 The signal x(t) is decomposed into several
IMFs based on the EMD method and the redundant IMFs
were removed based on the correlation coefficient And the
physical meaning of the effective IMFs can be found
Step 2 The HHT marginal spectrum of each IMF
component was calculated based on Hilbert transformation
And the IMF energy moment was calculated The opera-
tion state of the rotary kiln was determined according to
202
the IMF energy moment According to [16] the energy of
each IMF component can be calculated by the Eq (7)
2
1
N
i ijE k t c k t
(7)
where Δt is the period of data samples N is the total num-
ber of data samples and k represents the number of data
samples
The IMF energy moment can be calculated by
Eq (8)
1 2 1
n
i n iiE E E E E
T (8)
where
n
i iE1
is the summary energy of all the IMF
components of the signal n is the number of the effective
IMF components T is the percent of the energy of IMF
components in the whole signal energy
5 Experiment and discussions
The measurement system comprises an acquisi-
tion card the non-contact eddy current sensors the hall
sensor and the measuring software as shown in Fig 7 b
During the measurement the non-contact eddy current
sensor is mounted through fixture to keep the sensor probe
in the contact direction of roller and kiln tyre (y direction)
as shown in Fig 7 a and probe should be kept close
enough to the surface of the roller according to the eddy
current sensor range
a
b
Fig 7 a - The installation position (in the y direction) of the
displacement sensors and b - schematic diagram of
the experimental setup
The hall sensor is installed in a fixed position of
rotary kiln to interact with magnet mounted on the kiln
cylinder generating pulse signal per lap which is used to
synchronize the collected vibration signal and the rotation
of the rotary kiln Then the collected vibration signals are
sent by NI data acquisition card to the upper computer for
management and storage by Labview-based data acquisi-
tion software and SQL database
We did several experiments in cement plants in
China and the measured object was a rotary kiln which
consist three tyres The speed of the kiln cylinder was
35 r min while the supporting rollers were 105 r min
The vibration signals of all the supporting rollers were
collected based on the measurement system The sample
frequency of the channel was settled to 20 HZ
The kiln crank leading to the vibration of the
supporting rollers often takes place in the second and third
rollers Therefore for verifying the dynamics model of the
supporting rollers the vibration signal of the third right
supporting rollers was used to analyze as shown in Fig 8
Also the profile data of the cross section near to the third
station were collected The geometric centre base circle
and eccentricity can be calculated by the computational
algorithm proposed by literature [4 5]
Fig 8 Vibration signal of the third right roller
a
b
Fig 9 a - The calculation result of the section eccentricity
near to the third station b - the spectrum of the vi-
bration signal of third right supporting roller
005859HZ
Kiln harmonic
01758HZ
Roller harmonic
Section eccentricity
e=303mm
203
Based on the computational algorithm the eccen-
tricity of the cross section near to the third station is
e = 303 mm as shown in Fig 9 a It means that there
should be RH and KH components in the vibration signals
of the supporting rollers according to the numerical simu-
lation result We adopted FFT method to process the vibra-
tion signals of the third right roller as shown in Fig 9 b
And we can find two major frequency components
(005859 HZ and 01758 HZ) in the signals which are ba-
sically the same as the rotation frequencies of the rotary
kilnrsquos cylinder (05833 HZ) and supporting roller
(0175 HZ) respectively Eccentricity appeared in the cyl-
inderrsquos section and correspondingly KH component ap-
peared in the vibration signals of the supporting roller This
was the same as the simulation result and proved that the
model was correct And the physical map of in field indus-
try experiment was shown in Fig 10
Fig 10 Physical map of experiment for verifying the dy-
namics model of the supporting rollers
We processed the vibration data of all supporting
rollers based on empirical mode decomposition method
And the vibration signal of the third right supporting roller
was analyzed EMD processing results are shown in
Fig 11 After the vibration signals were processed with
EMD method the IMF components ranked from high to
low frequency In particular the specific physical meanings
of each IMF component are as follows IMF5 (frequency
005859 HZ) is harmonic component caused by the kiln
crank IMF4 (frequency 01758 HZ) is the vibration com-
ponent caused by the supporting roller shaft deflection
according to [17 18] IMF3 is the ripple deformation
component of the supporting rollerrsquos surface IMF2 is the
harmonic component of the supporting rollerrsquos surface
roughness IMF1 is the harmonic component of micro-
scopic deformation
Fig 11 The EMD decomposition result of the vibration
signal of the third right supporting roller
In order to decide the operation status of the rota-
ry kiln the IMF energy moment is proposed according to
the definition mentioned in section 4 And the proposed
IMF energy moment is T whose computa-
tion formulas is shown in (9)
5 4 3 2 1 E E E E E E E E (9)
where α represents the energy coefficient of the harmonic
component caused by kiln crank β represents the energy
coefficient of the harmonic component resulting from de-
flection of the supporting rollerrsquos shaft and λ represents
the energy coefficient of harmonic component of the sup-
porting rollerrsquos surface roughness and harmonic
Fig 11 Calculation results of IMF energy coefficient of the
supporting rollers
From the calculation result we can find that the
energy coefficient of IMF1 IMF2 and IMF3 components
(λ) representing the contour deformation of the second left
and right supporting rollers and the third right supporting
roller are great and the energy coefficient of IMF4 (β) and
IMF5 (α) components representing the kiln crank and de-
flection of the supporting rollerrsquos are relative small And
the energy coefficient of IMF4 and IMF5 of the second left
Eddy current sensor
Supporting roller
Laser sensor
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
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31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
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httpdxdoiorg101007978-3-319-10494-2_5
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50-55
4 Krystowczyk Z 2004 Geometry measurements of
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5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
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httpdxdoiorg103233SAV-2010-0573
9 Xuchang Jiang 2012 Adjustment of the supporting
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10 Guo C Al-Shudeifat MA Yan J Bergman
LA McFarland DM Butcher EA 2013 Appli-
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11 Gao Q Duan C Fan H Meng Q 2008 Rotating
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12 Liu B Riemenschneider S Xu Y 2006 Gearbox
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httpdxdoiorg101016jymssp200502003
13 Huang NE Shen Z Long SR Wu MC Shih
HH Zheng Q Liu HH 1998 The empirical
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hematical Physical and Engineering Sciences
454(1971) 903-995 The Royal Society
httpdxdoiorg101098rspa19980193
14 He D Li R Zhu J 2013 Plastic bearing fault di-
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IEEE Transactions on Industrial Electronics 60(8)
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15 Li R He D 2012 Rotational machine health moni-
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16 Bin GF Gao JJ Li XJ Dhillon BS 2012
Early fault diagnosis of rotating machinery based on
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httpdxdoidoiorg101016jymssp201108002
17 Xia C Wu Y Lu Q Ju B 2014 Surface cha-
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httpdxdoidoiorg101016jmeasurement2013080
66
18 Muralikrishnan B Raja J 2008 Computational
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Business Media 263 p
httpdxdoiorg101007978-1-84800-297-5
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
199
2 Physical model of the supporting rollers
21 The effect to supporting rollers of kiln operation
According to FMECA result the fault of the sup-
porting rollers is a main factor which can lead to the
breakdown of the rotary kiln [1-2] According to [3] the
fault of the supporting rollers is mainly caused by the kiln
crank generated by the internal thermal process of the ro-
tary kiln During long-term operation the profile of the
cylinder will change which will lead to misalignment be-
tween the geometric center and the rotation center thereby
causing the eccentricity of the cylinder section And the
dynamic load caused by the deformation of the cylinder
eccentricity gives rise to the vibration of the supporting
roller The snowball effect in the rotary kilnrsquos cylinder will
further intensify the vibration of the supporting rollers
According to [1] the materials will form a basic ball in the
kiln called the snowball effect during the operation of the
rotary kiln The ball moves slowly around the kilnrsquos axis
When the weight of the snowball exceeds the adhesive
force on the kiln coating and the snowball surface the
snowball will come off from the kiln coating Under ex-
treme conditions such a thermal effect may lead to signif-
icant load unbalance of the supporting rollers
Fig 2 shows the straightness deviation of the ro-
tary kiln we measured in a cement plant in China It can be
found that the straightness deviation of rotary kiln cylinder
was large due to various factors The supporting rollers in
the three stations of the rotary kiln are free from the re-
straint of the tyre When the snowball effect appears in the
rotary kilnrsquos cylinder the straightness deviation of the axis
will increase leading to heavy cyclic loads which will
cause the vibration of supporting rollers in the radial direc-
tion as shown in Fig 3 If the vibration amplitude is too
large the plain bearing may not make up the displacement
of the roller shaft so as to cause frictional heating in them
And the bearing alloy will melt with the high temperature
causing significant failure of the supporting rollers
Fig 2 The measurement result of straightness deviation of
the rotary kiln in a cement plant
Fig 3 The vibration of supporting rollers caused by the
Kiln crank effect
To establish the dynamic equation of the support-
ing rollers it is very important to describe the cyclic load
resulting from the kiln crankAccording to [2 4] the
change of the kiln cylinder profile is an important factor
resulting in the dynamic load and the eccentricity (e) can
be used as a main parameter for assessing the section pro-
file To establish the dynamic model of the supporting roll-
ers a simplified formula was put forward for the cyclic
load calculation And it can be expressed as
2
1 1 1f m e (1)
Where m1 is the equivalent unbalance mass at the
corresponding station ω1 is the kiln cylinderrsquos rotational
speed and e1 is the eccentricity of the cylinderrsquos cross sec-
tion
22 The equations of the supporting rollers
To establish the dynamic model of the low-speed
rotary kilnrsquos supporting system under cyclic load we es-
tablished a simplified model as shown in Fig 4 In Fig 4
supposing that the rotary kilnrsquos supporting roller is a disc
with a mass m the supporting shaft is an isotropic shaft
without mass and the left and right rollers at the same po-
sition of the rotary kiln bear the same load and that OXY is
the inertial coordinate system Oxy is the rotating coordi-
nate system O is the whirling center (rotation center) of
the supporting roller Orsquo is the centroid R is the radius of
the supporting roller e is the eccentricity of the center sec-
tion of the supporting roller We can derive the equation of
the supporting rollerrsquos vibration according to Lagranges
dynamical equations
a b
Fig 4 The model schematic of supporting rollers a - side
view b - front view
According to the force analysis for the supporting
rollers the external loads of them can be expressed by
Eqs (2)
2
1
2
1
n
j
n
j
F f cos tme cos t
f sin tme cos tQ
(2)
where f is the cyclic load caused by the kiln crank ω is the
rotation speed of the supporting roller and e is the eccen-
tricity of the supporting roller Based on Lagranges dy-
namical equations and formulas (2) we can derive the dy-
namic equation of the supporting roller as expressed by
Eq (3)
200
1 1
2 2
0 00
0 00
n
j
n
j
Fc km x x x
c km y Qy y
(3)
where k1 and k2 are the stiffness values of the supporting
roller in x and y directions c1 and c2 are the damping forc-
es of the supporting roller in x and y directions respec-
tively as we suppose the supporting roller is isotropous it
can be regarded that k1 = k2 c1 = c2 m is the equivalent
mass of the supporting roller
3 Numerical prediction for the response of supporting
rollers
31 The simulation parameters estimation
It is great important to carry out a careful estima-
tion of the physical parameter values of the supporting
rollers to perform a numerical simulation However it is
difficult to take this task as that the specific parameters of
the support rollers depend on the production the length
and the tyre number of a rotary kiln In this research we
take a qualitative analysis to the numerical simulation of a
three tryes rotary kiln with the production of
5000-6500 dt According to [9] the basic material of the
supporting rollers is ZG42GrMo and the elasticity modulus
of it is 209 times 105 MPa The mass density of the rollers is
786 times 10-6 kg mm3 and the radius is 1150 mm Based on
the above data we can obtain the approximate physical
parameter values of supporting rollers which are shown in
Table 1
Table 1
Estimation parameters of the supporting rollers
used for numerical simulations
Parameter Value
Rollers stiffness of x y axis k1 k2 148 times 105 N m
Rollers viscous damping of x y
axis c1 c2 692 times 104 Ns m
Equivalent mass of rollers m 405 times 104 kg
Equivalent imbalance mass of
station2 m1 797 times 105 kg
The rotating speed of the rollers ω 107 r min
The rotating speed of the kiln ω1 4 r min
Mass unbalance angle β 0 rad
32 Numerical analysis of the supporting rollers
In this section the dynamic response of the sup-
porting rollers under the influence of the kiln cylinder
crank was studies The influence of the cyclic load to sup-
porting rollers caused by thermal effects of the kiln cylin-
der was stimulated
As it is difficult to achieve analytical solution of
the complex dynamics equation the numerical methods
was used to solve the problem And the fourth-order
Runge-Kutta method [10] is selected to solve the Eq (10)
to obtain the dynamics response of the supporting rollers
The effect on the supporting rollers of the rotary
kiln crank was analyzed in this section According to sec-
tion II during the operation of the kiln it will change the
dimensional size as the result of the internal thermal pro-
cesses As the rotation center and the center of mass is not
overlap in the cylinder section thus producing section ec-
centricity Therefore the eccentricity of the cross section
can be used as a main parameter to represent the kiln crank
And we compared the vibration response of the supporting
roller under whether or not there is kiln crank And the
simulation result was shown in Fig 5 Furthermore the
relationship between the section eccentricity of the kiln
cylinder and the amplitude of the kiln harmonic and the
amplitude of the rollers harmonic was analyzed and the
result was shown in Fig 6
a
b
Fig 5 The vibration response in the y direction of the sup-
porting rollers when e1 = 3 and e1 = 10 mm a - time
domain b - frequency domain
Fig 6 Relationship between the section eccentricity of the
kiln cylinder and the amplitude of the kiln harmonic
and the amplitude of the rollers harmonic
From the above numerical simulation results it
can be found that
1) when there is kiln crank there will have a kiln
harmonics (KH) in the vibration signal
2) when the magnitude of the kiln harmonic
201
(KH) increased it is a sign that the crank of the rotary kiln
is being enhanced And it has larger deviations from the
normal operation in terms of eccentricity and deflections
from regular rotation axis in section corresponding to mon-
itored station
3) the frequency of kiln harmonic is consistent
with rotary kiln rotating speed while the frequency of roll-
ers harmonic is equal to the supporting rollers rotation
speed Therefore the operation condition of the rotary kiln
can be monitored by collecting the vibration signals of the
supporting rollers
4 Feature extraction using empirical mode
decomposition method
As mentioned in section 3 the vibration signals of
the supporting rollers contain multiple fault information
According to the numerical analysis for the supporting
rollers it can be found that the vibration signal mainly
includes the harmonic component caused by the kiln crank
and the harmonic component caused by the deflection of
the roller shaft In [17] authors pointed out that it also
contains the harmonic component of the surface character-
istic such as the harmonic component of waviness the
roughness and micro-irregularities In fact the vibration
signal are nonlinear non-stationary signal which are not
suitable processed by the traditional signal processing
method such as fast Fourier transform (FFT) or Wavelet
transform (WT) [12-14] In this research we proposed a
method for feature extraction of supporting rollers based
on empirical mode decomposition
41 Empirical mode decomposition
Empirical mode decomposition was first proposed
as a part of HilbertndashHuang transform (HHT) by Norden
Ehuang which is effective method to analysis the nonlin-
ear non-stationary signal [13] As the key part of HHT the
method of EMD to decompose signal is intuitive direct
and adaptive This decomposition method is based on local
characteristic of local time domain of signals Based on
this characteristic any linear stationary or nonlinear
non-stationary signal can be decomposed into a set of In-
trinsic Mode Functions (IMFs) which are amplitude and
frequency modulated signals It has been proven to be an
effective method in analyzing nonstationary signals for
rotational machine fault detection [15 16] According to
[15 16] each IMF satisfies two basic conditions
1) over the entire dataset the number of extreme
and the number of zero crossings must either be equal or
differ at most by one
2) at any time point the local mean value of the
envelope which defined by the average of the maximum
and minimum envelopes is zero
The specific processes of EMD are described as
follows
Step 1 For the given signal x(t) construct its up-
per envelope emax(t) and lower envelope emin(t) by connect-
ing all local maxima and local minima with cubic spline
functions And
11
2
max mine t e t
m
(4)
Step 2 Compute the envelopes mean m11 and
x(t) ndash m11 = h1(t) And the definition of IMF is proposed
mainly to get the physical meaning of the instantaneous
frequency
Step 3 If h1(t) satisfies the definition of IMF then
we can obtain the first-order IMF IMF1 = h1(t) And then
go to the next step In addition the IMF component
c1(t) = h1k(t) is saved If it is not the IMF repeat Steps 1ndash3
The stop condition for the iteration is given by
2
1
20
1
iji jT
t
i j
h t h tSD
h t
(5)
where hi(j-1)(t) and hij(t) denote the IMF candidates of the
j ndash 1 and j iterations respectively and usually SD is set
between 02 and 03
Step 4 Separate c1(t) from x(t) we could get
r1(t) = x(t) ndash c1(t) r1(t) is treated as the original data and
repeat the above processes the second IMF component c2(t)
of x(t) could be got Let us repeat the process as described
above for n times then n-IMFs of signal x(t) could be got
Step 5 The decomposition process can be stopped
when r(n)(t) becomes a monotonic function from which no
more IMF can be extracted We can finally obtain
1
n
i nix t c t r
(6)
Residue r(n)(t) is the mean trend of x(t) The IMFs
c1(t) c2(t) cn(t) include different frequency bands
ranging from high to low The frequency components con-
tained in each frequency band are different and they
change with the variation of signal x(t) while r(n)(t) repre-
sents the central tendency of signal x(t)
42 Feature extraction and fault diagnosis procedure
Numerical simulation results shown that the kiln
harmonic (KH) and the rollers harmonic (RH) will lead to
significant change as the kiln cylinder crank happens or the
rollers behavior changes Therefore the energy variation of
the kiln harmonic (KH) and the rollers harmonic (RH) of
the vibration signals can reflect the running condition of
the rotary kiln When the malfunction occur in a mechani-
cal equipment the energy of the vibration signal would
change strongly in some frequency bands but in other fre-
quency bands the energy maybe change weakly [12] Ac-
cording to [16] the IMF energy moment not only contains
the size of IMFs energy but also considers the distribution
of IMFrsquos energy change with the time parameter t It can
be used to express the energy distribution of the fault
characteristic frequency component for the vibration sig-
nals In this research the IMFrsquos energy moment is em-
ployed for fault diagnosis of the supporting rollers And the
procedures are summarized as follows
Step 1 The signal x(t) is decomposed into several
IMFs based on the EMD method and the redundant IMFs
were removed based on the correlation coefficient And the
physical meaning of the effective IMFs can be found
Step 2 The HHT marginal spectrum of each IMF
component was calculated based on Hilbert transformation
And the IMF energy moment was calculated The opera-
tion state of the rotary kiln was determined according to
202
the IMF energy moment According to [16] the energy of
each IMF component can be calculated by the Eq (7)
2
1
N
i ijE k t c k t
(7)
where Δt is the period of data samples N is the total num-
ber of data samples and k represents the number of data
samples
The IMF energy moment can be calculated by
Eq (8)
1 2 1
n
i n iiE E E E E
T (8)
where
n
i iE1
is the summary energy of all the IMF
components of the signal n is the number of the effective
IMF components T is the percent of the energy of IMF
components in the whole signal energy
5 Experiment and discussions
The measurement system comprises an acquisi-
tion card the non-contact eddy current sensors the hall
sensor and the measuring software as shown in Fig 7 b
During the measurement the non-contact eddy current
sensor is mounted through fixture to keep the sensor probe
in the contact direction of roller and kiln tyre (y direction)
as shown in Fig 7 a and probe should be kept close
enough to the surface of the roller according to the eddy
current sensor range
a
b
Fig 7 a - The installation position (in the y direction) of the
displacement sensors and b - schematic diagram of
the experimental setup
The hall sensor is installed in a fixed position of
rotary kiln to interact with magnet mounted on the kiln
cylinder generating pulse signal per lap which is used to
synchronize the collected vibration signal and the rotation
of the rotary kiln Then the collected vibration signals are
sent by NI data acquisition card to the upper computer for
management and storage by Labview-based data acquisi-
tion software and SQL database
We did several experiments in cement plants in
China and the measured object was a rotary kiln which
consist three tyres The speed of the kiln cylinder was
35 r min while the supporting rollers were 105 r min
The vibration signals of all the supporting rollers were
collected based on the measurement system The sample
frequency of the channel was settled to 20 HZ
The kiln crank leading to the vibration of the
supporting rollers often takes place in the second and third
rollers Therefore for verifying the dynamics model of the
supporting rollers the vibration signal of the third right
supporting rollers was used to analyze as shown in Fig 8
Also the profile data of the cross section near to the third
station were collected The geometric centre base circle
and eccentricity can be calculated by the computational
algorithm proposed by literature [4 5]
Fig 8 Vibration signal of the third right roller
a
b
Fig 9 a - The calculation result of the section eccentricity
near to the third station b - the spectrum of the vi-
bration signal of third right supporting roller
005859HZ
Kiln harmonic
01758HZ
Roller harmonic
Section eccentricity
e=303mm
203
Based on the computational algorithm the eccen-
tricity of the cross section near to the third station is
e = 303 mm as shown in Fig 9 a It means that there
should be RH and KH components in the vibration signals
of the supporting rollers according to the numerical simu-
lation result We adopted FFT method to process the vibra-
tion signals of the third right roller as shown in Fig 9 b
And we can find two major frequency components
(005859 HZ and 01758 HZ) in the signals which are ba-
sically the same as the rotation frequencies of the rotary
kilnrsquos cylinder (05833 HZ) and supporting roller
(0175 HZ) respectively Eccentricity appeared in the cyl-
inderrsquos section and correspondingly KH component ap-
peared in the vibration signals of the supporting roller This
was the same as the simulation result and proved that the
model was correct And the physical map of in field indus-
try experiment was shown in Fig 10
Fig 10 Physical map of experiment for verifying the dy-
namics model of the supporting rollers
We processed the vibration data of all supporting
rollers based on empirical mode decomposition method
And the vibration signal of the third right supporting roller
was analyzed EMD processing results are shown in
Fig 11 After the vibration signals were processed with
EMD method the IMF components ranked from high to
low frequency In particular the specific physical meanings
of each IMF component are as follows IMF5 (frequency
005859 HZ) is harmonic component caused by the kiln
crank IMF4 (frequency 01758 HZ) is the vibration com-
ponent caused by the supporting roller shaft deflection
according to [17 18] IMF3 is the ripple deformation
component of the supporting rollerrsquos surface IMF2 is the
harmonic component of the supporting rollerrsquos surface
roughness IMF1 is the harmonic component of micro-
scopic deformation
Fig 11 The EMD decomposition result of the vibration
signal of the third right supporting roller
In order to decide the operation status of the rota-
ry kiln the IMF energy moment is proposed according to
the definition mentioned in section 4 And the proposed
IMF energy moment is T whose computa-
tion formulas is shown in (9)
5 4 3 2 1 E E E E E E E E (9)
where α represents the energy coefficient of the harmonic
component caused by kiln crank β represents the energy
coefficient of the harmonic component resulting from de-
flection of the supporting rollerrsquos shaft and λ represents
the energy coefficient of harmonic component of the sup-
porting rollerrsquos surface roughness and harmonic
Fig 11 Calculation results of IMF energy coefficient of the
supporting rollers
From the calculation result we can find that the
energy coefficient of IMF1 IMF2 and IMF3 components
(λ) representing the contour deformation of the second left
and right supporting rollers and the third right supporting
roller are great and the energy coefficient of IMF4 (β) and
IMF5 (α) components representing the kiln crank and de-
flection of the supporting rollerrsquos are relative small And
the energy coefficient of IMF4 and IMF5 of the second left
Eddy current sensor
Supporting roller
Laser sensor
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
References
1 Rusinski E Stamboliska Z Moczko P 2013
Proactive control system of condition of low-speed
cement machinery Automation in Construction
31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
nes Springer International Publishing 186 p
httpdxdoiorg101007978-3-319-10494-2_5
3 Gebhart WM Stutz T 2007 Process know-
how-routine support roller shaft deflection measure-
ments-surprising results ZKG International 60(7)
50-55
4 Krystowczyk Z 2004 Geometry measurements of
kiln shell in dynamic conditions Cement amp Building
Materials 16 34-37
5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
feature extraction based on EMD method Engineering
Letters 23(4) 283-291
6 Świtalski M 2010 The measurement of shells elastic
ovality as essential element of diagnostic of rotary
drums technical state Diagnostyka 1(53) 37-47
7 Žiga A Karač A Vukojević D 2013 Analytical
and numerical stress analysis of the rotary kiln ring
Tehnički Vjesnik 20(6) 941-946
8 Li X Shen Y Wang S 2011 Dynamic modeling
and analysis of the large-scale rotary machine with
multi-supporting Shock and Vibration 18(1-2) 53-62
httpdxdoiorg103233SAV-2010-0573
9 Xuchang Jiang 2012 Adjustment of the supporting
rollers for the rotary kiln China building material
press
10 Guo C Al-Shudeifat MA Yan J Bergman
LA McFarland DM Butcher EA 2013 Appli-
cation of empirical mode decomposition to a Jeffcott
rotor with a breathing crack Journal of Sound and
Vibration 332(16) 3881-3892
httpdxdoiorg101016jjsv201302031
11 Gao Q Duan C Fan H Meng Q 2008 Rotating
machine fault diagnosis using empirical mode decom-
position Mechanical Systems and Signal Processing
22(5) 1072-1081
httpdxdoiorg101016jymssp200710003
12 Liu B Riemenschneider S Xu Y 2006 Gearbox
fault diagnosis using empirical mode decomposition
and Hilbert spectrum Mechanical Systems and Signal
Processing 20(3) 718-734
httpdxdoiorg101016jymssp200502003
13 Huang NE Shen Z Long SR Wu MC Shih
HH Zheng Q Liu HH 1998 The empirical
mode decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series analysis In
Proceedings of the Royal Society of London A Mat-
hematical Physical and Engineering Sciences
454(1971) 903-995 The Royal Society
httpdxdoiorg101098rspa19980193
14 He D Li R Zhu J 2013 Plastic bearing fault di-
agnosis based on a two-step data mining approach
IEEE Transactions on Industrial Electronics 60(8)
3429-3440
httpdxdoiorg101109TIE20122192894
15 Li R He D 2012 Rotational machine health moni-
toring and fault detection using EMD-based acoustic
emission feature quantification IEEE Transactions on
Instrumentation and Measurement 61(4) 990-1001
httpdxdoiorg101109TIM20112179819
16 Bin GF Gao JJ Li XJ Dhillon BS 2012
Early fault diagnosis of rotating machinery based on
wavelet packetsmdashEmpirical mode decomposition fea-
ture extraction and neural network Mechanical
Systems and Signal Processing 27 696-711
httpdxdoidoiorg101016jymssp201108002
17 Xia C Wu Y Lu Q Ju B 2014 Surface cha-
racteristic profile extraction based on HilbertndashHuang
transform Measurement 47 306-313
httpdxdoidoiorg101016jmeasurement2013080
66
18 Muralikrishnan B Raja J 2008 Computational
Surface and Roundness Metrology Springer Science amp
Business Media 263 p
httpdxdoiorg101007978-1-84800-297-5
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
200
1 1
2 2
0 00
0 00
n
j
n
j
Fc km x x x
c km y Qy y
(3)
where k1 and k2 are the stiffness values of the supporting
roller in x and y directions c1 and c2 are the damping forc-
es of the supporting roller in x and y directions respec-
tively as we suppose the supporting roller is isotropous it
can be regarded that k1 = k2 c1 = c2 m is the equivalent
mass of the supporting roller
3 Numerical prediction for the response of supporting
rollers
31 The simulation parameters estimation
It is great important to carry out a careful estima-
tion of the physical parameter values of the supporting
rollers to perform a numerical simulation However it is
difficult to take this task as that the specific parameters of
the support rollers depend on the production the length
and the tyre number of a rotary kiln In this research we
take a qualitative analysis to the numerical simulation of a
three tryes rotary kiln with the production of
5000-6500 dt According to [9] the basic material of the
supporting rollers is ZG42GrMo and the elasticity modulus
of it is 209 times 105 MPa The mass density of the rollers is
786 times 10-6 kg mm3 and the radius is 1150 mm Based on
the above data we can obtain the approximate physical
parameter values of supporting rollers which are shown in
Table 1
Table 1
Estimation parameters of the supporting rollers
used for numerical simulations
Parameter Value
Rollers stiffness of x y axis k1 k2 148 times 105 N m
Rollers viscous damping of x y
axis c1 c2 692 times 104 Ns m
Equivalent mass of rollers m 405 times 104 kg
Equivalent imbalance mass of
station2 m1 797 times 105 kg
The rotating speed of the rollers ω 107 r min
The rotating speed of the kiln ω1 4 r min
Mass unbalance angle β 0 rad
32 Numerical analysis of the supporting rollers
In this section the dynamic response of the sup-
porting rollers under the influence of the kiln cylinder
crank was studies The influence of the cyclic load to sup-
porting rollers caused by thermal effects of the kiln cylin-
der was stimulated
As it is difficult to achieve analytical solution of
the complex dynamics equation the numerical methods
was used to solve the problem And the fourth-order
Runge-Kutta method [10] is selected to solve the Eq (10)
to obtain the dynamics response of the supporting rollers
The effect on the supporting rollers of the rotary
kiln crank was analyzed in this section According to sec-
tion II during the operation of the kiln it will change the
dimensional size as the result of the internal thermal pro-
cesses As the rotation center and the center of mass is not
overlap in the cylinder section thus producing section ec-
centricity Therefore the eccentricity of the cross section
can be used as a main parameter to represent the kiln crank
And we compared the vibration response of the supporting
roller under whether or not there is kiln crank And the
simulation result was shown in Fig 5 Furthermore the
relationship between the section eccentricity of the kiln
cylinder and the amplitude of the kiln harmonic and the
amplitude of the rollers harmonic was analyzed and the
result was shown in Fig 6
a
b
Fig 5 The vibration response in the y direction of the sup-
porting rollers when e1 = 3 and e1 = 10 mm a - time
domain b - frequency domain
Fig 6 Relationship between the section eccentricity of the
kiln cylinder and the amplitude of the kiln harmonic
and the amplitude of the rollers harmonic
From the above numerical simulation results it
can be found that
1) when there is kiln crank there will have a kiln
harmonics (KH) in the vibration signal
2) when the magnitude of the kiln harmonic
201
(KH) increased it is a sign that the crank of the rotary kiln
is being enhanced And it has larger deviations from the
normal operation in terms of eccentricity and deflections
from regular rotation axis in section corresponding to mon-
itored station
3) the frequency of kiln harmonic is consistent
with rotary kiln rotating speed while the frequency of roll-
ers harmonic is equal to the supporting rollers rotation
speed Therefore the operation condition of the rotary kiln
can be monitored by collecting the vibration signals of the
supporting rollers
4 Feature extraction using empirical mode
decomposition method
As mentioned in section 3 the vibration signals of
the supporting rollers contain multiple fault information
According to the numerical analysis for the supporting
rollers it can be found that the vibration signal mainly
includes the harmonic component caused by the kiln crank
and the harmonic component caused by the deflection of
the roller shaft In [17] authors pointed out that it also
contains the harmonic component of the surface character-
istic such as the harmonic component of waviness the
roughness and micro-irregularities In fact the vibration
signal are nonlinear non-stationary signal which are not
suitable processed by the traditional signal processing
method such as fast Fourier transform (FFT) or Wavelet
transform (WT) [12-14] In this research we proposed a
method for feature extraction of supporting rollers based
on empirical mode decomposition
41 Empirical mode decomposition
Empirical mode decomposition was first proposed
as a part of HilbertndashHuang transform (HHT) by Norden
Ehuang which is effective method to analysis the nonlin-
ear non-stationary signal [13] As the key part of HHT the
method of EMD to decompose signal is intuitive direct
and adaptive This decomposition method is based on local
characteristic of local time domain of signals Based on
this characteristic any linear stationary or nonlinear
non-stationary signal can be decomposed into a set of In-
trinsic Mode Functions (IMFs) which are amplitude and
frequency modulated signals It has been proven to be an
effective method in analyzing nonstationary signals for
rotational machine fault detection [15 16] According to
[15 16] each IMF satisfies two basic conditions
1) over the entire dataset the number of extreme
and the number of zero crossings must either be equal or
differ at most by one
2) at any time point the local mean value of the
envelope which defined by the average of the maximum
and minimum envelopes is zero
The specific processes of EMD are described as
follows
Step 1 For the given signal x(t) construct its up-
per envelope emax(t) and lower envelope emin(t) by connect-
ing all local maxima and local minima with cubic spline
functions And
11
2
max mine t e t
m
(4)
Step 2 Compute the envelopes mean m11 and
x(t) ndash m11 = h1(t) And the definition of IMF is proposed
mainly to get the physical meaning of the instantaneous
frequency
Step 3 If h1(t) satisfies the definition of IMF then
we can obtain the first-order IMF IMF1 = h1(t) And then
go to the next step In addition the IMF component
c1(t) = h1k(t) is saved If it is not the IMF repeat Steps 1ndash3
The stop condition for the iteration is given by
2
1
20
1
iji jT
t
i j
h t h tSD
h t
(5)
where hi(j-1)(t) and hij(t) denote the IMF candidates of the
j ndash 1 and j iterations respectively and usually SD is set
between 02 and 03
Step 4 Separate c1(t) from x(t) we could get
r1(t) = x(t) ndash c1(t) r1(t) is treated as the original data and
repeat the above processes the second IMF component c2(t)
of x(t) could be got Let us repeat the process as described
above for n times then n-IMFs of signal x(t) could be got
Step 5 The decomposition process can be stopped
when r(n)(t) becomes a monotonic function from which no
more IMF can be extracted We can finally obtain
1
n
i nix t c t r
(6)
Residue r(n)(t) is the mean trend of x(t) The IMFs
c1(t) c2(t) cn(t) include different frequency bands
ranging from high to low The frequency components con-
tained in each frequency band are different and they
change with the variation of signal x(t) while r(n)(t) repre-
sents the central tendency of signal x(t)
42 Feature extraction and fault diagnosis procedure
Numerical simulation results shown that the kiln
harmonic (KH) and the rollers harmonic (RH) will lead to
significant change as the kiln cylinder crank happens or the
rollers behavior changes Therefore the energy variation of
the kiln harmonic (KH) and the rollers harmonic (RH) of
the vibration signals can reflect the running condition of
the rotary kiln When the malfunction occur in a mechani-
cal equipment the energy of the vibration signal would
change strongly in some frequency bands but in other fre-
quency bands the energy maybe change weakly [12] Ac-
cording to [16] the IMF energy moment not only contains
the size of IMFs energy but also considers the distribution
of IMFrsquos energy change with the time parameter t It can
be used to express the energy distribution of the fault
characteristic frequency component for the vibration sig-
nals In this research the IMFrsquos energy moment is em-
ployed for fault diagnosis of the supporting rollers And the
procedures are summarized as follows
Step 1 The signal x(t) is decomposed into several
IMFs based on the EMD method and the redundant IMFs
were removed based on the correlation coefficient And the
physical meaning of the effective IMFs can be found
Step 2 The HHT marginal spectrum of each IMF
component was calculated based on Hilbert transformation
And the IMF energy moment was calculated The opera-
tion state of the rotary kiln was determined according to
202
the IMF energy moment According to [16] the energy of
each IMF component can be calculated by the Eq (7)
2
1
N
i ijE k t c k t
(7)
where Δt is the period of data samples N is the total num-
ber of data samples and k represents the number of data
samples
The IMF energy moment can be calculated by
Eq (8)
1 2 1
n
i n iiE E E E E
T (8)
where
n
i iE1
is the summary energy of all the IMF
components of the signal n is the number of the effective
IMF components T is the percent of the energy of IMF
components in the whole signal energy
5 Experiment and discussions
The measurement system comprises an acquisi-
tion card the non-contact eddy current sensors the hall
sensor and the measuring software as shown in Fig 7 b
During the measurement the non-contact eddy current
sensor is mounted through fixture to keep the sensor probe
in the contact direction of roller and kiln tyre (y direction)
as shown in Fig 7 a and probe should be kept close
enough to the surface of the roller according to the eddy
current sensor range
a
b
Fig 7 a - The installation position (in the y direction) of the
displacement sensors and b - schematic diagram of
the experimental setup
The hall sensor is installed in a fixed position of
rotary kiln to interact with magnet mounted on the kiln
cylinder generating pulse signal per lap which is used to
synchronize the collected vibration signal and the rotation
of the rotary kiln Then the collected vibration signals are
sent by NI data acquisition card to the upper computer for
management and storage by Labview-based data acquisi-
tion software and SQL database
We did several experiments in cement plants in
China and the measured object was a rotary kiln which
consist three tyres The speed of the kiln cylinder was
35 r min while the supporting rollers were 105 r min
The vibration signals of all the supporting rollers were
collected based on the measurement system The sample
frequency of the channel was settled to 20 HZ
The kiln crank leading to the vibration of the
supporting rollers often takes place in the second and third
rollers Therefore for verifying the dynamics model of the
supporting rollers the vibration signal of the third right
supporting rollers was used to analyze as shown in Fig 8
Also the profile data of the cross section near to the third
station were collected The geometric centre base circle
and eccentricity can be calculated by the computational
algorithm proposed by literature [4 5]
Fig 8 Vibration signal of the third right roller
a
b
Fig 9 a - The calculation result of the section eccentricity
near to the third station b - the spectrum of the vi-
bration signal of third right supporting roller
005859HZ
Kiln harmonic
01758HZ
Roller harmonic
Section eccentricity
e=303mm
203
Based on the computational algorithm the eccen-
tricity of the cross section near to the third station is
e = 303 mm as shown in Fig 9 a It means that there
should be RH and KH components in the vibration signals
of the supporting rollers according to the numerical simu-
lation result We adopted FFT method to process the vibra-
tion signals of the third right roller as shown in Fig 9 b
And we can find two major frequency components
(005859 HZ and 01758 HZ) in the signals which are ba-
sically the same as the rotation frequencies of the rotary
kilnrsquos cylinder (05833 HZ) and supporting roller
(0175 HZ) respectively Eccentricity appeared in the cyl-
inderrsquos section and correspondingly KH component ap-
peared in the vibration signals of the supporting roller This
was the same as the simulation result and proved that the
model was correct And the physical map of in field indus-
try experiment was shown in Fig 10
Fig 10 Physical map of experiment for verifying the dy-
namics model of the supporting rollers
We processed the vibration data of all supporting
rollers based on empirical mode decomposition method
And the vibration signal of the third right supporting roller
was analyzed EMD processing results are shown in
Fig 11 After the vibration signals were processed with
EMD method the IMF components ranked from high to
low frequency In particular the specific physical meanings
of each IMF component are as follows IMF5 (frequency
005859 HZ) is harmonic component caused by the kiln
crank IMF4 (frequency 01758 HZ) is the vibration com-
ponent caused by the supporting roller shaft deflection
according to [17 18] IMF3 is the ripple deformation
component of the supporting rollerrsquos surface IMF2 is the
harmonic component of the supporting rollerrsquos surface
roughness IMF1 is the harmonic component of micro-
scopic deformation
Fig 11 The EMD decomposition result of the vibration
signal of the third right supporting roller
In order to decide the operation status of the rota-
ry kiln the IMF energy moment is proposed according to
the definition mentioned in section 4 And the proposed
IMF energy moment is T whose computa-
tion formulas is shown in (9)
5 4 3 2 1 E E E E E E E E (9)
where α represents the energy coefficient of the harmonic
component caused by kiln crank β represents the energy
coefficient of the harmonic component resulting from de-
flection of the supporting rollerrsquos shaft and λ represents
the energy coefficient of harmonic component of the sup-
porting rollerrsquos surface roughness and harmonic
Fig 11 Calculation results of IMF energy coefficient of the
supporting rollers
From the calculation result we can find that the
energy coefficient of IMF1 IMF2 and IMF3 components
(λ) representing the contour deformation of the second left
and right supporting rollers and the third right supporting
roller are great and the energy coefficient of IMF4 (β) and
IMF5 (α) components representing the kiln crank and de-
flection of the supporting rollerrsquos are relative small And
the energy coefficient of IMF4 and IMF5 of the second left
Eddy current sensor
Supporting roller
Laser sensor
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
References
1 Rusinski E Stamboliska Z Moczko P 2013
Proactive control system of condition of low-speed
cement machinery Automation in Construction
31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
nes Springer International Publishing 186 p
httpdxdoiorg101007978-3-319-10494-2_5
3 Gebhart WM Stutz T 2007 Process know-
how-routine support roller shaft deflection measure-
ments-surprising results ZKG International 60(7)
50-55
4 Krystowczyk Z 2004 Geometry measurements of
kiln shell in dynamic conditions Cement amp Building
Materials 16 34-37
5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
feature extraction based on EMD method Engineering
Letters 23(4) 283-291
6 Świtalski M 2010 The measurement of shells elastic
ovality as essential element of diagnostic of rotary
drums technical state Diagnostyka 1(53) 37-47
7 Žiga A Karač A Vukojević D 2013 Analytical
and numerical stress analysis of the rotary kiln ring
Tehnički Vjesnik 20(6) 941-946
8 Li X Shen Y Wang S 2011 Dynamic modeling
and analysis of the large-scale rotary machine with
multi-supporting Shock and Vibration 18(1-2) 53-62
httpdxdoiorg103233SAV-2010-0573
9 Xuchang Jiang 2012 Adjustment of the supporting
rollers for the rotary kiln China building material
press
10 Guo C Al-Shudeifat MA Yan J Bergman
LA McFarland DM Butcher EA 2013 Appli-
cation of empirical mode decomposition to a Jeffcott
rotor with a breathing crack Journal of Sound and
Vibration 332(16) 3881-3892
httpdxdoiorg101016jjsv201302031
11 Gao Q Duan C Fan H Meng Q 2008 Rotating
machine fault diagnosis using empirical mode decom-
position Mechanical Systems and Signal Processing
22(5) 1072-1081
httpdxdoiorg101016jymssp200710003
12 Liu B Riemenschneider S Xu Y 2006 Gearbox
fault diagnosis using empirical mode decomposition
and Hilbert spectrum Mechanical Systems and Signal
Processing 20(3) 718-734
httpdxdoiorg101016jymssp200502003
13 Huang NE Shen Z Long SR Wu MC Shih
HH Zheng Q Liu HH 1998 The empirical
mode decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series analysis In
Proceedings of the Royal Society of London A Mat-
hematical Physical and Engineering Sciences
454(1971) 903-995 The Royal Society
httpdxdoiorg101098rspa19980193
14 He D Li R Zhu J 2013 Plastic bearing fault di-
agnosis based on a two-step data mining approach
IEEE Transactions on Industrial Electronics 60(8)
3429-3440
httpdxdoiorg101109TIE20122192894
15 Li R He D 2012 Rotational machine health moni-
toring and fault detection using EMD-based acoustic
emission feature quantification IEEE Transactions on
Instrumentation and Measurement 61(4) 990-1001
httpdxdoiorg101109TIM20112179819
16 Bin GF Gao JJ Li XJ Dhillon BS 2012
Early fault diagnosis of rotating machinery based on
wavelet packetsmdashEmpirical mode decomposition fea-
ture extraction and neural network Mechanical
Systems and Signal Processing 27 696-711
httpdxdoidoiorg101016jymssp201108002
17 Xia C Wu Y Lu Q Ju B 2014 Surface cha-
racteristic profile extraction based on HilbertndashHuang
transform Measurement 47 306-313
httpdxdoidoiorg101016jmeasurement2013080
66
18 Muralikrishnan B Raja J 2008 Computational
Surface and Roundness Metrology Springer Science amp
Business Media 263 p
httpdxdoiorg101007978-1-84800-297-5
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
201
(KH) increased it is a sign that the crank of the rotary kiln
is being enhanced And it has larger deviations from the
normal operation in terms of eccentricity and deflections
from regular rotation axis in section corresponding to mon-
itored station
3) the frequency of kiln harmonic is consistent
with rotary kiln rotating speed while the frequency of roll-
ers harmonic is equal to the supporting rollers rotation
speed Therefore the operation condition of the rotary kiln
can be monitored by collecting the vibration signals of the
supporting rollers
4 Feature extraction using empirical mode
decomposition method
As mentioned in section 3 the vibration signals of
the supporting rollers contain multiple fault information
According to the numerical analysis for the supporting
rollers it can be found that the vibration signal mainly
includes the harmonic component caused by the kiln crank
and the harmonic component caused by the deflection of
the roller shaft In [17] authors pointed out that it also
contains the harmonic component of the surface character-
istic such as the harmonic component of waviness the
roughness and micro-irregularities In fact the vibration
signal are nonlinear non-stationary signal which are not
suitable processed by the traditional signal processing
method such as fast Fourier transform (FFT) or Wavelet
transform (WT) [12-14] In this research we proposed a
method for feature extraction of supporting rollers based
on empirical mode decomposition
41 Empirical mode decomposition
Empirical mode decomposition was first proposed
as a part of HilbertndashHuang transform (HHT) by Norden
Ehuang which is effective method to analysis the nonlin-
ear non-stationary signal [13] As the key part of HHT the
method of EMD to decompose signal is intuitive direct
and adaptive This decomposition method is based on local
characteristic of local time domain of signals Based on
this characteristic any linear stationary or nonlinear
non-stationary signal can be decomposed into a set of In-
trinsic Mode Functions (IMFs) which are amplitude and
frequency modulated signals It has been proven to be an
effective method in analyzing nonstationary signals for
rotational machine fault detection [15 16] According to
[15 16] each IMF satisfies two basic conditions
1) over the entire dataset the number of extreme
and the number of zero crossings must either be equal or
differ at most by one
2) at any time point the local mean value of the
envelope which defined by the average of the maximum
and minimum envelopes is zero
The specific processes of EMD are described as
follows
Step 1 For the given signal x(t) construct its up-
per envelope emax(t) and lower envelope emin(t) by connect-
ing all local maxima and local minima with cubic spline
functions And
11
2
max mine t e t
m
(4)
Step 2 Compute the envelopes mean m11 and
x(t) ndash m11 = h1(t) And the definition of IMF is proposed
mainly to get the physical meaning of the instantaneous
frequency
Step 3 If h1(t) satisfies the definition of IMF then
we can obtain the first-order IMF IMF1 = h1(t) And then
go to the next step In addition the IMF component
c1(t) = h1k(t) is saved If it is not the IMF repeat Steps 1ndash3
The stop condition for the iteration is given by
2
1
20
1
iji jT
t
i j
h t h tSD
h t
(5)
where hi(j-1)(t) and hij(t) denote the IMF candidates of the
j ndash 1 and j iterations respectively and usually SD is set
between 02 and 03
Step 4 Separate c1(t) from x(t) we could get
r1(t) = x(t) ndash c1(t) r1(t) is treated as the original data and
repeat the above processes the second IMF component c2(t)
of x(t) could be got Let us repeat the process as described
above for n times then n-IMFs of signal x(t) could be got
Step 5 The decomposition process can be stopped
when r(n)(t) becomes a monotonic function from which no
more IMF can be extracted We can finally obtain
1
n
i nix t c t r
(6)
Residue r(n)(t) is the mean trend of x(t) The IMFs
c1(t) c2(t) cn(t) include different frequency bands
ranging from high to low The frequency components con-
tained in each frequency band are different and they
change with the variation of signal x(t) while r(n)(t) repre-
sents the central tendency of signal x(t)
42 Feature extraction and fault diagnosis procedure
Numerical simulation results shown that the kiln
harmonic (KH) and the rollers harmonic (RH) will lead to
significant change as the kiln cylinder crank happens or the
rollers behavior changes Therefore the energy variation of
the kiln harmonic (KH) and the rollers harmonic (RH) of
the vibration signals can reflect the running condition of
the rotary kiln When the malfunction occur in a mechani-
cal equipment the energy of the vibration signal would
change strongly in some frequency bands but in other fre-
quency bands the energy maybe change weakly [12] Ac-
cording to [16] the IMF energy moment not only contains
the size of IMFs energy but also considers the distribution
of IMFrsquos energy change with the time parameter t It can
be used to express the energy distribution of the fault
characteristic frequency component for the vibration sig-
nals In this research the IMFrsquos energy moment is em-
ployed for fault diagnosis of the supporting rollers And the
procedures are summarized as follows
Step 1 The signal x(t) is decomposed into several
IMFs based on the EMD method and the redundant IMFs
were removed based on the correlation coefficient And the
physical meaning of the effective IMFs can be found
Step 2 The HHT marginal spectrum of each IMF
component was calculated based on Hilbert transformation
And the IMF energy moment was calculated The opera-
tion state of the rotary kiln was determined according to
202
the IMF energy moment According to [16] the energy of
each IMF component can be calculated by the Eq (7)
2
1
N
i ijE k t c k t
(7)
where Δt is the period of data samples N is the total num-
ber of data samples and k represents the number of data
samples
The IMF energy moment can be calculated by
Eq (8)
1 2 1
n
i n iiE E E E E
T (8)
where
n
i iE1
is the summary energy of all the IMF
components of the signal n is the number of the effective
IMF components T is the percent of the energy of IMF
components in the whole signal energy
5 Experiment and discussions
The measurement system comprises an acquisi-
tion card the non-contact eddy current sensors the hall
sensor and the measuring software as shown in Fig 7 b
During the measurement the non-contact eddy current
sensor is mounted through fixture to keep the sensor probe
in the contact direction of roller and kiln tyre (y direction)
as shown in Fig 7 a and probe should be kept close
enough to the surface of the roller according to the eddy
current sensor range
a
b
Fig 7 a - The installation position (in the y direction) of the
displacement sensors and b - schematic diagram of
the experimental setup
The hall sensor is installed in a fixed position of
rotary kiln to interact with magnet mounted on the kiln
cylinder generating pulse signal per lap which is used to
synchronize the collected vibration signal and the rotation
of the rotary kiln Then the collected vibration signals are
sent by NI data acquisition card to the upper computer for
management and storage by Labview-based data acquisi-
tion software and SQL database
We did several experiments in cement plants in
China and the measured object was a rotary kiln which
consist three tyres The speed of the kiln cylinder was
35 r min while the supporting rollers were 105 r min
The vibration signals of all the supporting rollers were
collected based on the measurement system The sample
frequency of the channel was settled to 20 HZ
The kiln crank leading to the vibration of the
supporting rollers often takes place in the second and third
rollers Therefore for verifying the dynamics model of the
supporting rollers the vibration signal of the third right
supporting rollers was used to analyze as shown in Fig 8
Also the profile data of the cross section near to the third
station were collected The geometric centre base circle
and eccentricity can be calculated by the computational
algorithm proposed by literature [4 5]
Fig 8 Vibration signal of the third right roller
a
b
Fig 9 a - The calculation result of the section eccentricity
near to the third station b - the spectrum of the vi-
bration signal of third right supporting roller
005859HZ
Kiln harmonic
01758HZ
Roller harmonic
Section eccentricity
e=303mm
203
Based on the computational algorithm the eccen-
tricity of the cross section near to the third station is
e = 303 mm as shown in Fig 9 a It means that there
should be RH and KH components in the vibration signals
of the supporting rollers according to the numerical simu-
lation result We adopted FFT method to process the vibra-
tion signals of the third right roller as shown in Fig 9 b
And we can find two major frequency components
(005859 HZ and 01758 HZ) in the signals which are ba-
sically the same as the rotation frequencies of the rotary
kilnrsquos cylinder (05833 HZ) and supporting roller
(0175 HZ) respectively Eccentricity appeared in the cyl-
inderrsquos section and correspondingly KH component ap-
peared in the vibration signals of the supporting roller This
was the same as the simulation result and proved that the
model was correct And the physical map of in field indus-
try experiment was shown in Fig 10
Fig 10 Physical map of experiment for verifying the dy-
namics model of the supporting rollers
We processed the vibration data of all supporting
rollers based on empirical mode decomposition method
And the vibration signal of the third right supporting roller
was analyzed EMD processing results are shown in
Fig 11 After the vibration signals were processed with
EMD method the IMF components ranked from high to
low frequency In particular the specific physical meanings
of each IMF component are as follows IMF5 (frequency
005859 HZ) is harmonic component caused by the kiln
crank IMF4 (frequency 01758 HZ) is the vibration com-
ponent caused by the supporting roller shaft deflection
according to [17 18] IMF3 is the ripple deformation
component of the supporting rollerrsquos surface IMF2 is the
harmonic component of the supporting rollerrsquos surface
roughness IMF1 is the harmonic component of micro-
scopic deformation
Fig 11 The EMD decomposition result of the vibration
signal of the third right supporting roller
In order to decide the operation status of the rota-
ry kiln the IMF energy moment is proposed according to
the definition mentioned in section 4 And the proposed
IMF energy moment is T whose computa-
tion formulas is shown in (9)
5 4 3 2 1 E E E E E E E E (9)
where α represents the energy coefficient of the harmonic
component caused by kiln crank β represents the energy
coefficient of the harmonic component resulting from de-
flection of the supporting rollerrsquos shaft and λ represents
the energy coefficient of harmonic component of the sup-
porting rollerrsquos surface roughness and harmonic
Fig 11 Calculation results of IMF energy coefficient of the
supporting rollers
From the calculation result we can find that the
energy coefficient of IMF1 IMF2 and IMF3 components
(λ) representing the contour deformation of the second left
and right supporting rollers and the third right supporting
roller are great and the energy coefficient of IMF4 (β) and
IMF5 (α) components representing the kiln crank and de-
flection of the supporting rollerrsquos are relative small And
the energy coefficient of IMF4 and IMF5 of the second left
Eddy current sensor
Supporting roller
Laser sensor
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
References
1 Rusinski E Stamboliska Z Moczko P 2013
Proactive control system of condition of low-speed
cement machinery Automation in Construction
31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
nes Springer International Publishing 186 p
httpdxdoiorg101007978-3-319-10494-2_5
3 Gebhart WM Stutz T 2007 Process know-
how-routine support roller shaft deflection measure-
ments-surprising results ZKG International 60(7)
50-55
4 Krystowczyk Z 2004 Geometry measurements of
kiln shell in dynamic conditions Cement amp Building
Materials 16 34-37
5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
feature extraction based on EMD method Engineering
Letters 23(4) 283-291
6 Świtalski M 2010 The measurement of shells elastic
ovality as essential element of diagnostic of rotary
drums technical state Diagnostyka 1(53) 37-47
7 Žiga A Karač A Vukojević D 2013 Analytical
and numerical stress analysis of the rotary kiln ring
Tehnički Vjesnik 20(6) 941-946
8 Li X Shen Y Wang S 2011 Dynamic modeling
and analysis of the large-scale rotary machine with
multi-supporting Shock and Vibration 18(1-2) 53-62
httpdxdoiorg103233SAV-2010-0573
9 Xuchang Jiang 2012 Adjustment of the supporting
rollers for the rotary kiln China building material
press
10 Guo C Al-Shudeifat MA Yan J Bergman
LA McFarland DM Butcher EA 2013 Appli-
cation of empirical mode decomposition to a Jeffcott
rotor with a breathing crack Journal of Sound and
Vibration 332(16) 3881-3892
httpdxdoiorg101016jjsv201302031
11 Gao Q Duan C Fan H Meng Q 2008 Rotating
machine fault diagnosis using empirical mode decom-
position Mechanical Systems and Signal Processing
22(5) 1072-1081
httpdxdoiorg101016jymssp200710003
12 Liu B Riemenschneider S Xu Y 2006 Gearbox
fault diagnosis using empirical mode decomposition
and Hilbert spectrum Mechanical Systems and Signal
Processing 20(3) 718-734
httpdxdoiorg101016jymssp200502003
13 Huang NE Shen Z Long SR Wu MC Shih
HH Zheng Q Liu HH 1998 The empirical
mode decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series analysis In
Proceedings of the Royal Society of London A Mat-
hematical Physical and Engineering Sciences
454(1971) 903-995 The Royal Society
httpdxdoiorg101098rspa19980193
14 He D Li R Zhu J 2013 Plastic bearing fault di-
agnosis based on a two-step data mining approach
IEEE Transactions on Industrial Electronics 60(8)
3429-3440
httpdxdoiorg101109TIE20122192894
15 Li R He D 2012 Rotational machine health moni-
toring and fault detection using EMD-based acoustic
emission feature quantification IEEE Transactions on
Instrumentation and Measurement 61(4) 990-1001
httpdxdoiorg101109TIM20112179819
16 Bin GF Gao JJ Li XJ Dhillon BS 2012
Early fault diagnosis of rotating machinery based on
wavelet packetsmdashEmpirical mode decomposition fea-
ture extraction and neural network Mechanical
Systems and Signal Processing 27 696-711
httpdxdoidoiorg101016jymssp201108002
17 Xia C Wu Y Lu Q Ju B 2014 Surface cha-
racteristic profile extraction based on HilbertndashHuang
transform Measurement 47 306-313
httpdxdoidoiorg101016jmeasurement2013080
66
18 Muralikrishnan B Raja J 2008 Computational
Surface and Roundness Metrology Springer Science amp
Business Media 263 p
httpdxdoiorg101007978-1-84800-297-5
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
202
the IMF energy moment According to [16] the energy of
each IMF component can be calculated by the Eq (7)
2
1
N
i ijE k t c k t
(7)
where Δt is the period of data samples N is the total num-
ber of data samples and k represents the number of data
samples
The IMF energy moment can be calculated by
Eq (8)
1 2 1
n
i n iiE E E E E
T (8)
where
n
i iE1
is the summary energy of all the IMF
components of the signal n is the number of the effective
IMF components T is the percent of the energy of IMF
components in the whole signal energy
5 Experiment and discussions
The measurement system comprises an acquisi-
tion card the non-contact eddy current sensors the hall
sensor and the measuring software as shown in Fig 7 b
During the measurement the non-contact eddy current
sensor is mounted through fixture to keep the sensor probe
in the contact direction of roller and kiln tyre (y direction)
as shown in Fig 7 a and probe should be kept close
enough to the surface of the roller according to the eddy
current sensor range
a
b
Fig 7 a - The installation position (in the y direction) of the
displacement sensors and b - schematic diagram of
the experimental setup
The hall sensor is installed in a fixed position of
rotary kiln to interact with magnet mounted on the kiln
cylinder generating pulse signal per lap which is used to
synchronize the collected vibration signal and the rotation
of the rotary kiln Then the collected vibration signals are
sent by NI data acquisition card to the upper computer for
management and storage by Labview-based data acquisi-
tion software and SQL database
We did several experiments in cement plants in
China and the measured object was a rotary kiln which
consist three tyres The speed of the kiln cylinder was
35 r min while the supporting rollers were 105 r min
The vibration signals of all the supporting rollers were
collected based on the measurement system The sample
frequency of the channel was settled to 20 HZ
The kiln crank leading to the vibration of the
supporting rollers often takes place in the second and third
rollers Therefore for verifying the dynamics model of the
supporting rollers the vibration signal of the third right
supporting rollers was used to analyze as shown in Fig 8
Also the profile data of the cross section near to the third
station were collected The geometric centre base circle
and eccentricity can be calculated by the computational
algorithm proposed by literature [4 5]
Fig 8 Vibration signal of the third right roller
a
b
Fig 9 a - The calculation result of the section eccentricity
near to the third station b - the spectrum of the vi-
bration signal of third right supporting roller
005859HZ
Kiln harmonic
01758HZ
Roller harmonic
Section eccentricity
e=303mm
203
Based on the computational algorithm the eccen-
tricity of the cross section near to the third station is
e = 303 mm as shown in Fig 9 a It means that there
should be RH and KH components in the vibration signals
of the supporting rollers according to the numerical simu-
lation result We adopted FFT method to process the vibra-
tion signals of the third right roller as shown in Fig 9 b
And we can find two major frequency components
(005859 HZ and 01758 HZ) in the signals which are ba-
sically the same as the rotation frequencies of the rotary
kilnrsquos cylinder (05833 HZ) and supporting roller
(0175 HZ) respectively Eccentricity appeared in the cyl-
inderrsquos section and correspondingly KH component ap-
peared in the vibration signals of the supporting roller This
was the same as the simulation result and proved that the
model was correct And the physical map of in field indus-
try experiment was shown in Fig 10
Fig 10 Physical map of experiment for verifying the dy-
namics model of the supporting rollers
We processed the vibration data of all supporting
rollers based on empirical mode decomposition method
And the vibration signal of the third right supporting roller
was analyzed EMD processing results are shown in
Fig 11 After the vibration signals were processed with
EMD method the IMF components ranked from high to
low frequency In particular the specific physical meanings
of each IMF component are as follows IMF5 (frequency
005859 HZ) is harmonic component caused by the kiln
crank IMF4 (frequency 01758 HZ) is the vibration com-
ponent caused by the supporting roller shaft deflection
according to [17 18] IMF3 is the ripple deformation
component of the supporting rollerrsquos surface IMF2 is the
harmonic component of the supporting rollerrsquos surface
roughness IMF1 is the harmonic component of micro-
scopic deformation
Fig 11 The EMD decomposition result of the vibration
signal of the third right supporting roller
In order to decide the operation status of the rota-
ry kiln the IMF energy moment is proposed according to
the definition mentioned in section 4 And the proposed
IMF energy moment is T whose computa-
tion formulas is shown in (9)
5 4 3 2 1 E E E E E E E E (9)
where α represents the energy coefficient of the harmonic
component caused by kiln crank β represents the energy
coefficient of the harmonic component resulting from de-
flection of the supporting rollerrsquos shaft and λ represents
the energy coefficient of harmonic component of the sup-
porting rollerrsquos surface roughness and harmonic
Fig 11 Calculation results of IMF energy coefficient of the
supporting rollers
From the calculation result we can find that the
energy coefficient of IMF1 IMF2 and IMF3 components
(λ) representing the contour deformation of the second left
and right supporting rollers and the third right supporting
roller are great and the energy coefficient of IMF4 (β) and
IMF5 (α) components representing the kiln crank and de-
flection of the supporting rollerrsquos are relative small And
the energy coefficient of IMF4 and IMF5 of the second left
Eddy current sensor
Supporting roller
Laser sensor
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
References
1 Rusinski E Stamboliska Z Moczko P 2013
Proactive control system of condition of low-speed
cement machinery Automation in Construction
31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
nes Springer International Publishing 186 p
httpdxdoiorg101007978-3-319-10494-2_5
3 Gebhart WM Stutz T 2007 Process know-
how-routine support roller shaft deflection measure-
ments-surprising results ZKG International 60(7)
50-55
4 Krystowczyk Z 2004 Geometry measurements of
kiln shell in dynamic conditions Cement amp Building
Materials 16 34-37
5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
feature extraction based on EMD method Engineering
Letters 23(4) 283-291
6 Świtalski M 2010 The measurement of shells elastic
ovality as essential element of diagnostic of rotary
drums technical state Diagnostyka 1(53) 37-47
7 Žiga A Karač A Vukojević D 2013 Analytical
and numerical stress analysis of the rotary kiln ring
Tehnički Vjesnik 20(6) 941-946
8 Li X Shen Y Wang S 2011 Dynamic modeling
and analysis of the large-scale rotary machine with
multi-supporting Shock and Vibration 18(1-2) 53-62
httpdxdoiorg103233SAV-2010-0573
9 Xuchang Jiang 2012 Adjustment of the supporting
rollers for the rotary kiln China building material
press
10 Guo C Al-Shudeifat MA Yan J Bergman
LA McFarland DM Butcher EA 2013 Appli-
cation of empirical mode decomposition to a Jeffcott
rotor with a breathing crack Journal of Sound and
Vibration 332(16) 3881-3892
httpdxdoiorg101016jjsv201302031
11 Gao Q Duan C Fan H Meng Q 2008 Rotating
machine fault diagnosis using empirical mode decom-
position Mechanical Systems and Signal Processing
22(5) 1072-1081
httpdxdoiorg101016jymssp200710003
12 Liu B Riemenschneider S Xu Y 2006 Gearbox
fault diagnosis using empirical mode decomposition
and Hilbert spectrum Mechanical Systems and Signal
Processing 20(3) 718-734
httpdxdoiorg101016jymssp200502003
13 Huang NE Shen Z Long SR Wu MC Shih
HH Zheng Q Liu HH 1998 The empirical
mode decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series analysis In
Proceedings of the Royal Society of London A Mat-
hematical Physical and Engineering Sciences
454(1971) 903-995 The Royal Society
httpdxdoiorg101098rspa19980193
14 He D Li R Zhu J 2013 Plastic bearing fault di-
agnosis based on a two-step data mining approach
IEEE Transactions on Industrial Electronics 60(8)
3429-3440
httpdxdoiorg101109TIE20122192894
15 Li R He D 2012 Rotational machine health moni-
toring and fault detection using EMD-based acoustic
emission feature quantification IEEE Transactions on
Instrumentation and Measurement 61(4) 990-1001
httpdxdoiorg101109TIM20112179819
16 Bin GF Gao JJ Li XJ Dhillon BS 2012
Early fault diagnosis of rotating machinery based on
wavelet packetsmdashEmpirical mode decomposition fea-
ture extraction and neural network Mechanical
Systems and Signal Processing 27 696-711
httpdxdoidoiorg101016jymssp201108002
17 Xia C Wu Y Lu Q Ju B 2014 Surface cha-
racteristic profile extraction based on HilbertndashHuang
transform Measurement 47 306-313
httpdxdoidoiorg101016jmeasurement2013080
66
18 Muralikrishnan B Raja J 2008 Computational
Surface and Roundness Metrology Springer Science amp
Business Media 263 p
httpdxdoiorg101007978-1-84800-297-5
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
203
Based on the computational algorithm the eccen-
tricity of the cross section near to the third station is
e = 303 mm as shown in Fig 9 a It means that there
should be RH and KH components in the vibration signals
of the supporting rollers according to the numerical simu-
lation result We adopted FFT method to process the vibra-
tion signals of the third right roller as shown in Fig 9 b
And we can find two major frequency components
(005859 HZ and 01758 HZ) in the signals which are ba-
sically the same as the rotation frequencies of the rotary
kilnrsquos cylinder (05833 HZ) and supporting roller
(0175 HZ) respectively Eccentricity appeared in the cyl-
inderrsquos section and correspondingly KH component ap-
peared in the vibration signals of the supporting roller This
was the same as the simulation result and proved that the
model was correct And the physical map of in field indus-
try experiment was shown in Fig 10
Fig 10 Physical map of experiment for verifying the dy-
namics model of the supporting rollers
We processed the vibration data of all supporting
rollers based on empirical mode decomposition method
And the vibration signal of the third right supporting roller
was analyzed EMD processing results are shown in
Fig 11 After the vibration signals were processed with
EMD method the IMF components ranked from high to
low frequency In particular the specific physical meanings
of each IMF component are as follows IMF5 (frequency
005859 HZ) is harmonic component caused by the kiln
crank IMF4 (frequency 01758 HZ) is the vibration com-
ponent caused by the supporting roller shaft deflection
according to [17 18] IMF3 is the ripple deformation
component of the supporting rollerrsquos surface IMF2 is the
harmonic component of the supporting rollerrsquos surface
roughness IMF1 is the harmonic component of micro-
scopic deformation
Fig 11 The EMD decomposition result of the vibration
signal of the third right supporting roller
In order to decide the operation status of the rota-
ry kiln the IMF energy moment is proposed according to
the definition mentioned in section 4 And the proposed
IMF energy moment is T whose computa-
tion formulas is shown in (9)
5 4 3 2 1 E E E E E E E E (9)
where α represents the energy coefficient of the harmonic
component caused by kiln crank β represents the energy
coefficient of the harmonic component resulting from de-
flection of the supporting rollerrsquos shaft and λ represents
the energy coefficient of harmonic component of the sup-
porting rollerrsquos surface roughness and harmonic
Fig 11 Calculation results of IMF energy coefficient of the
supporting rollers
From the calculation result we can find that the
energy coefficient of IMF1 IMF2 and IMF3 components
(λ) representing the contour deformation of the second left
and right supporting rollers and the third right supporting
roller are great and the energy coefficient of IMF4 (β) and
IMF5 (α) components representing the kiln crank and de-
flection of the supporting rollerrsquos are relative small And
the energy coefficient of IMF4 and IMF5 of the second left
Eddy current sensor
Supporting roller
Laser sensor
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
References
1 Rusinski E Stamboliska Z Moczko P 2013
Proactive control system of condition of low-speed
cement machinery Automation in Construction
31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
nes Springer International Publishing 186 p
httpdxdoiorg101007978-3-319-10494-2_5
3 Gebhart WM Stutz T 2007 Process know-
how-routine support roller shaft deflection measure-
ments-surprising results ZKG International 60(7)
50-55
4 Krystowczyk Z 2004 Geometry measurements of
kiln shell in dynamic conditions Cement amp Building
Materials 16 34-37
5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
feature extraction based on EMD method Engineering
Letters 23(4) 283-291
6 Świtalski M 2010 The measurement of shells elastic
ovality as essential element of diagnostic of rotary
drums technical state Diagnostyka 1(53) 37-47
7 Žiga A Karač A Vukojević D 2013 Analytical
and numerical stress analysis of the rotary kiln ring
Tehnički Vjesnik 20(6) 941-946
8 Li X Shen Y Wang S 2011 Dynamic modeling
and analysis of the large-scale rotary machine with
multi-supporting Shock and Vibration 18(1-2) 53-62
httpdxdoiorg103233SAV-2010-0573
9 Xuchang Jiang 2012 Adjustment of the supporting
rollers for the rotary kiln China building material
press
10 Guo C Al-Shudeifat MA Yan J Bergman
LA McFarland DM Butcher EA 2013 Appli-
cation of empirical mode decomposition to a Jeffcott
rotor with a breathing crack Journal of Sound and
Vibration 332(16) 3881-3892
httpdxdoiorg101016jjsv201302031
11 Gao Q Duan C Fan H Meng Q 2008 Rotating
machine fault diagnosis using empirical mode decom-
position Mechanical Systems and Signal Processing
22(5) 1072-1081
httpdxdoiorg101016jymssp200710003
12 Liu B Riemenschneider S Xu Y 2006 Gearbox
fault diagnosis using empirical mode decomposition
and Hilbert spectrum Mechanical Systems and Signal
Processing 20(3) 718-734
httpdxdoiorg101016jymssp200502003
13 Huang NE Shen Z Long SR Wu MC Shih
HH Zheng Q Liu HH 1998 The empirical
mode decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series analysis In
Proceedings of the Royal Society of London A Mat-
hematical Physical and Engineering Sciences
454(1971) 903-995 The Royal Society
httpdxdoiorg101098rspa19980193
14 He D Li R Zhu J 2013 Plastic bearing fault di-
agnosis based on a two-step data mining approach
IEEE Transactions on Industrial Electronics 60(8)
3429-3440
httpdxdoiorg101109TIE20122192894
15 Li R He D 2012 Rotational machine health moni-
toring and fault detection using EMD-based acoustic
emission feature quantification IEEE Transactions on
Instrumentation and Measurement 61(4) 990-1001
httpdxdoiorg101109TIM20112179819
16 Bin GF Gao JJ Li XJ Dhillon BS 2012
Early fault diagnosis of rotating machinery based on
wavelet packetsmdashEmpirical mode decomposition fea-
ture extraction and neural network Mechanical
Systems and Signal Processing 27 696-711
httpdxdoidoiorg101016jymssp201108002
17 Xia C Wu Y Lu Q Ju B 2014 Surface cha-
racteristic profile extraction based on HilbertndashHuang
transform Measurement 47 306-313
httpdxdoidoiorg101016jmeasurement2013080
66
18 Muralikrishnan B Raja J 2008 Computational
Surface and Roundness Metrology Springer Science amp
Business Media 263 p
httpdxdoiorg101007978-1-84800-297-5
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
204
supporting roller are great as shown in Fig 12 It shows
that the contour of the second left and right supporting
rollers and the third right supporting roller deformed to
some extent due to heavy load on them but the impact
vibration resulting from the kilnrsquos thermal effect is small
However the impact vibration of the third left supporting
roller is big due to the heavy kiln crank If no maintenance
measures are taken the bearing of the supporting rollerrsquos
bearing may burn out and even melt due to the high tem-
perature
6 Conclusion
The operation condition of the rotary kiln can be
reflected by monitoring the vibration signals of the sup-
porting rollers as they are core components of it In order
to extract the feature of the vibration signals the numerical
simulation of the supporting rollers was analyzed and a
signal processed method based on EMD was proposed
From the above simulation and experimental results the
contributions and conclusion of this research are made as
follows
1) The numerical simulation result indicated that
when there is kiln crank there will have a kiln harmonics
(RH) in the vibration signal When the kiln crank enhance
the amplitude of kiln harmonics (RH) will increases while
the rollers harmonics (RH) almost has no change
2) The changes of the kiln harmonics and rollers
harmonics reflect the energy variation of vibration signals
when the rotary kiln is in different running statuses
Therefore a fault diagnosis method based on EMD was
proposed The signal was decomposed into a serial of IMF
components based on EMD An analysis was made over
energy distribution of fault features under different fre-
quency bands and the IMF energy moment was calculated
to determine the operating state of the rotary kiln
3) The simulation and experimental results indi-
cated that the proposed method could be used to extract the
feature for the vibration signals of the supporting rollers
effectively whichprovide a new method for the fault diag-
nosis of the low speed machinery like the rotary kiln
References
1 Rusinski E Stamboliska Z Moczko P 2013
Proactive control system of condition of low-speed
cement machinery Automation in Construction
31 313-324
httpdxdoiorg101016jautcon201212001
2 Stamboliska Z Rusiński E Moczko P 2015
Proactive Condition Monitoring of Low-Speed Machi-
nes Springer International Publishing 186 p
httpdxdoiorg101007978-3-319-10494-2_5
3 Gebhart WM Stutz T 2007 Process know-
how-routine support roller shaft deflection measure-
ments-surprising results ZKG International 60(7)
50-55
4 Krystowczyk Z 2004 Geometry measurements of
kiln shell in dynamic conditions Cement amp Building
Materials 16 34-37
5 Kai Zheng Yun Zhang Chen Zhao Lei Liu 2015
Rotary kiln cylinder deformation measurement and
feature extraction based on EMD method Engineering
Letters 23(4) 283-291
6 Świtalski M 2010 The measurement of shells elastic
ovality as essential element of diagnostic of rotary
drums technical state Diagnostyka 1(53) 37-47
7 Žiga A Karač A Vukojević D 2013 Analytical
and numerical stress analysis of the rotary kiln ring
Tehnički Vjesnik 20(6) 941-946
8 Li X Shen Y Wang S 2011 Dynamic modeling
and analysis of the large-scale rotary machine with
multi-supporting Shock and Vibration 18(1-2) 53-62
httpdxdoiorg103233SAV-2010-0573
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205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016
205
Kai Zheng Yun Zhang Chen Zhao Tianliang Li
FAULT DIAGNOSIS FOR SUPPORTING ROLLERS OF
THE ROTARY KILN USING THE DYNAMIC MODEL
AND EMPIRICAL MODE DECOMPOSITION
S u m m a r y
Rotary kiln is key equipment widely used in the
cement metallurgical and environmental protection indus-
try The operation state of the rotary kiln was largely de-
termined by the working condition of supporting rollers
This paper models the vibration mechanism of the sup-
porting rollers under the rotary kiln crank caused by the
internal thermal process Based on the numerical analysis
a methodology based on empirical mode decomposition
(EMD) for the fault diagnosis of the supporting rollers was
proposed By using EMD the complicated vibration signal
of the kiln can be decomposed into a number of intrinsic
mode functions (IMFs) An analysis was made over the
energy moment of IMF components to indicate the energy
variation of the kiln harmonic and the roller harmonic of
the vibration signals Simulation and in field experiment
results proved that the proposed method provided a validi-
ty of the approach for the condition monitoring and fault
diagnosis of the low-speed machinery like the rotary kiln
Keywords Supporting rollers fault diagnosis numerical
analysis empirical mode decomposition vibration moni-
toring
Received September 08 2015
Accepted May 11 2016